A Liouville theorem for non local elliptic equations

Louis Dupaigne; Yannick Sire

A Liouville theorem for non local elliptic equations

Analysis of PDEs 2009-09-10 v1

Authors: Louis Dupaigne , Yannick Sire

Abstract

We prove a Liouville-type theorem for bounded stable solutions $v \in C^2(\R^n)$ of elliptic equations of the type (-\Delta)^s v= f(v)\qquad {in $\R^n$ ,} where $s \in (0,1)$ {and $f$ is any nonnegative function}. The operator $(-\Delta)^s$ stands for the fractional Laplacian, a pseudo-differential operator of symbol $|\xi |^{2s}$ .

Keywords

liouville theorem fractional laplacian elliptic partial differential equations

Cite

@article{arxiv.0909.1650,
  title  = {A Liouville theorem for non local elliptic equations},
  author = {Louis Dupaigne and Yannick Sire},
  journal= {arXiv preprint arXiv:0909.1650},
  year   = {2009}
}

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